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Reproducing Kernel Method for Fractional Riccati Differential Equations

Author

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  • X. Y. Li
  • B. Y. Wu
  • R. T. Wang

Abstract

This paper is devoted to a new numerical method for fractional Riccati differential equations. The method combines the reproducing kernel method and the quasilinearization technique. Its main advantage is that it can produce good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results are compared with some existing methods to show the accuracy and effectiveness of the present method.

Suggested Citation

  • X. Y. Li & B. Y. Wu & R. T. Wang, 2014. "Reproducing Kernel Method for Fractional Riccati Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:970967
    DOI: 10.1155/2014/970967
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    References listed on IDEAS

    as
    1. Dumitru Baleanu & J. A. Tenreiro Machado & Carlo Cattani & Mihaela Cristina Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, January.
    2. Omar Abu Arqub & Mohammed Al-Smadi & Shaher Momani, 2012. "Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, September.
    3. Mustafa Inc & Ali Akgül & Adem Kiliçman, 2013. "A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Mustafa Inc & Ali Akgül & Adem Kiliçman, 2013. "A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, February.
    5. Omar Abu Arqub & Mohammed Al-Smadi & Shaher Momani, 2012. "Application of Reproducing Kernel Method for Solving Nonlinear Fredholm‐Volterra Integrodifferential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Dumitru Baleanu & J. A. Tenreiro Machado & Carlo Cattani & Mihaela Cristina Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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    Cited by:

    1. Yu-Lan Wang & Hao Yu & Fu-Gui Tan & Shanshan Qu, 2014. "Solving a Class of Singularly Perturbed Partial Differential Equation by Using the Perturbation Method and Reproducing Kernel Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Yulan Wang & Hao Yu & Fugui Tan & Shuguang Li, 2014. "Using an Effective Numerical Method for Solving a Class of Lane‐Emden Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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